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I suppose this is already known, but I discover it by myself:
If you take a grid of points from a 2d plane (just like you do to evaluate a set of points in a escape-time fractal), and then, without using any formula at all, just extracting the decimals from each x and y value to evaluate them, you get a fractal pattern.

e.g. for each point (x,y), iterate:

p=p+1 // the decimal place to extract

and this is a method for extracting a decimal at position 'p'
and making it a positive 1 digit integer:

xx=abs(floor(x*(10^p))-floor(x*(10^p)/10)*10)
yy=abs(floor(y*(10^p))-floor(y*(10^p)/10)*10)

(use floor() or int() or whatever that cuts out the decimal part)

then set up a bailout condition like this:

xx+yy>10

and coloring based on escape time, you get this Sierpinski-like pattern:



Maybe just a curiosity, but I wanted to share it with you, folks.

Thanks, Ken

This one is made using only absolute values of x,y and iterating z=z+xx-yy

This is an example code for UF:

decimalextraction {
init:
float x=real(#pixel)
float y=imag(#pixel)
int p=0

loop:
p=p+1
xx=abs(trunc(x*(10^p))-trunc(x*(10^p)/10)*10)
yy=abs(trunc(y*(10^p))-trunc(y*(10^p)/10)*10)
z=xx+yy ; (or z=z+xx-yy for the second image I posted)

bailout:
|z|<100
}

(Use multi-pass linear drawing method and turn off periodicity checking)

A different coloring method, and with scaled up pixels (that means I lowered the resolution), to see the patterns better.



To change the resolution of the x-y values in UF, I used:

newx=trunc(x*res)/res
newy=trunc(y*res)/res

For higher values of 'res', more resolution.
The patterns also change when you change the resolution, because new values have different fractional parts.
I'll make a simple movie to show this.

Do you mean in the "10^pos" part?

One thing I'm not sure is if I'm calling this in the proper way. I mean "decimal extraction", because in spanish we refer to the digits of the fractional part of a number as "decimals". Perhaps in english I must say that I'm extracting the "fractional digits"?

Kali, cool movie!

I think decimal extraction is a good name as long as you're using base 10.

[Edit: Removed an ill-conceived comment about aliasing.]

Regards,
Ken

Kali, what you've written makes sense. When I saw your movie, I was reminded of aliasing artifacts, which are usually undesirable. However, aliasing seems to be the source of your interesting patterns in this case.

Nice example, Kali. I believe your picture does illustrate a moiré pattern (a type of aliasing).